In the classical operator theory of MC, the transition function (probability) \( P (x,\cdot ) \)  is assumed to be a countably additive measure with respect to the second argument. At the same time, in the economic theory of games, developed since the 1960s by L. Dubbins L. Savage [1]} and their numerous students and followers, it became necessary to involve in the construction and study of specific random processes and finitely additive probability measures. In particular, in the paper [2]}, some constructions of finitely additive measures close to Markov chains were constructed and investigated.
